Behaviour of Random Error

Assume that all measurements are free of gross error and corrected for all systematic error.

	Practical Case	Theoretical Case
No. Of Observation	n->finite number	n→∞
Variable	Random Sample	Random Variable
Estimate	Mean	True value
Errors	Residuals	True Errors
Spread of Errors	Relative Frequency	Relative Frequency
	Probability Distribution Histogram	Probability Distribution Function

where,

Graphical example of

i. Probability distribution histogram

ii. Probability distribution function